From Direct method:
Class interval 
Mid value (x_{i}) 
f_{i} 
f_{i}x_{i} 
0  10 
5 
20 
100 
10  20 
15 
24 
360 
20  30 
25 
40 
1000 
40  50 
45 
20 
900 






N = 140 
\(\sum\)f_{i}x_{i} = 3620 
Mean = \(\frac{\sum f_ix_i}{N}\)
\(=\frac{3620}{140}=25.857\)
Assumed mean method:
let assumed mean (A) = 25
Mean = A + \(\frac{\sum f_iu_i}{N}\)
Class interval 
Mid value (x_{i}) 
u_{i} = xi  A 
f_{i} 
f_{i}u_{i} 
0  10 
5 
20 
20 
400 
10  20 
15 
10 
24 
240 
20  30 
25 
0 
40 
0 
30  40 
35 
10 
36 
360 
40  50 
45 
20 
20 
400 



N = 140 
\(\sum\)f_{i}u_{i} = 120 
Mean = A + \(\frac{\sum f_ix_i}{N}\)
\(=25+\frac{120}{140}=25+0.857\)
\(=25.857\)
Step deviation method: Let the assumed mean (A) = 25
Class interval 
Mid value (x_{i}) 
d_{i} = x_{i}  A = x_{i}  25 
u_{i} = \(\frac{xi25}{10}\) 
Frequency (f_{i}) 
f_{i}u_{i} 
0  10 
5 
20 
2 
20 
40 
10  20 
15 
10 
1 
24 
24 
20  30 
25 
0 
0 
40 
0 
30  40 
35 
10 
1 
36 
36 
40  50 
45 
20 
2 
20 
40 




N = 140 
\(\sum\)f_{i}u_{i} = 12 
Mean = A + \(\frac{\sum f_iu_i}{N}\times h\)
\(=25+0.857=25.857\)
\(=25+\frac{12}{140}\times10\)
\(=25+0.857=25.857\)